Proving that this set is a Dedekind cut.

[jdinatale]

Homework Statement

Homework Equations

In the above proplem, A is a dedekind cut.

To be a cut:
1. $A \not= \mathbf{Q}$ and $A \not = \emptyset$
2. If $r \in A$, then all $s \in A$ for all $s \in \mathbf{Q}$ such that $s < r$
3. A has no maximum


I know the 3 properties by heart, but the set -A is so unwieldy, that I'm having difficulty proving each of these properties.

 

[Hurkyl]

Then try things step-by-step. First, carefully write out what it is to be proven, incorporating the definition of -A...